The hydrogen line emission at the shock is taken from the models of [1]}. These apply the non-LTE radiation-hydrodynamical simulations of [2]} to the shock at the surface of an accreting planet. Through detailed calculations of chemical reactions and electron transitions in hydrogen atoms, the [2]} models calculate the cooling in the disequilibrium region immediately below the hydrodynamical shock, corresponding roughly to the downstream part of the Zel'dovich spike [4]}.
See Figure REF c.
This provides high-resolution profiles and line-integrated fluxes for 55 hydrogen lines in the series of Lyman, Balmer, Paschen, Brackett, etc.,
which are emitted from the shock towards the observer. These line profiles thus serve as the input for our calculation of
the radiative transfer
(Equation () below),
and will be seen as the black dashed lines in Figures REF –REF . The line-integrated luminosity \({L_{\textnormal {H}\,\alpha }} \)  as a function of \(\dot{M} \)  and \(M_{\mathrm {p}}\)  is shown in Figure 7 of [1]} and constitutes one of their main results.
